Approach a Miracle (Correct Video)

[@SudokuSleuth]

Apologies for the confusion this morning, I hope you enjoy the video and puzzle! 😀

[@chrisbrogan3307]

That was just fantastic!!!!

[@colleenscottcarmello5103]

**500 SUBS!!!!!! Congratulations!!!

[@SudokuSleuth]

Thanks you!

[@psiphiorg]

When I saw this on the CTC channel and read the description, I had a few insights before I opened the puzzle that led to a very quick solve, I want to say something like three minutes. (When I opened the link here, it didn't show my previous solve and time, so I don't have the exact time.) My first insight was that, because there is one 9 in each column, and each skyscraper is of a different height, those must match up one-to-one. So the 9 skyscraper clue would have the digit 9 in row 1, the 4 skyscraper clue would have it in row 6, and so on. Next, every cell between the bottom of the grid and the 9 must be visible, otherwise there would be two columns with the same skyscraper height. My next insight was more of an intuition at first. It seemed likely that the columns would have to be in consecutive ascending order as you go up the column. After thinking about that for a moment, it did seem more likely, for the reason that you explain with the examples in columns 1 and 2. After confirming that, then my next insight was that each group of three columns had to have their 9 digits in the same rows mod 3. For example, because column 3 had its 9 in row 9, that meant columns 1 and 2 had to have their 9 digits in rows 3 and 6 in some order. That's because the lower digits, which had to be in consecutive ascending order, would otherwise overlap. Columns 4, 5, and 6 then had to have their 9's in rows 2, 5, and 8 in some order (after placing the 9 in box 8). And that left rows 1, 4, and 7 for the last three columns. After figuring out where the 9's went with those constraints and the queen move, the only thing left was to figure out the digits above the 9 in each column. I would probably classify this as a "hunch" more than an insight... my guess was that the rest of the digits just had to start with 1 and also go up consecutively toward the top. Rather than try to figure out if I could confirm this hunch logically, I just placed the digits as quickly as my little fingers could go, and lo and behold, it was right. Only after finishing the puzzle did I go back and determine whether this was required or just a thematic choice by the designer that I had lucked into. It turned out to be required, for basically the same reason the column below the 9 had to be in consecutive ascending order. For example, the column where the 9 was in row 2 had used all the digits from 2-8 below it, so there was only one cell in the column left for the digit 1. In the column where 9 was in the 3, there were two rows for digits 1 and 2, and we had already placed the 1 in row 1, so that forced the 1 and 2 in that column. And so on. I really loved the thought that went into constructing this puzzle with these constraints, even though I basically did my fastest speed run ever in solving it. I appreciated both Simon's solve path and yours, and enjoyed hearing you figure out and explain your thought process along the way.

[@SudokuSleuth]

Nice work. If the Sudoku Pad puzzle doesn't have a solution, after I solve it I create a new link with the solution for the channel. That's why sometimes my links don't quite match what you may see on other channels / LMD.

[@colleenscottcarmello5103]

Super great puzzle!! Loved it!

[@neil2796]

I watched the CtC solve but didn't solve it then. It might have made the solve easier because I knew the ending but it was still fun. I don't think it's anti knight, but it is entropy in the rows.

[@jdyerjdyer]

A blazing 7 minutes and 40 seconds! Helps that I've seen similar miracles before...spoiler: that and the fact that it says nine thermometers all different lengths with one per column all starting in row 9. That forces the whole set as you end up with one in order from 1 to 9, one in order from 2 to 9... until there is just one with a single 9. The skyscraper clues and the diagonal constraint sort the order very quickly and from there it is just a matter of ribboning up the remaining digits 1 to x for each column, again forced in order due to the other constraints. This one really is "who can type the numbers the fastest" once the order is determined within the first few minutes. I wonder if a different miracle one could be made that is less forced at first? Maybe a five only odd thermos and four only even thermos (all vertical with the bulb at the bottom of each) and have just a few even and odd squares in the grid give the placement?

[@annek3296]

A small nit to pick from the other side of the pond - the monument in the thumbnail being approached by Sleuth is the JEFFERSON Memorial, not the LINCOLN Memorial. BTW, I think Jefferson, being of a very mathematical problem-solving bent, would have enjoyed Sudoku in general, & this particular solve in particular!

[@SudokuSleuth]

Ooh, thanks for the correction!

[@nicksharpe7924]

Can someone explain how one can automatically assume that all thermos, and the numbers above them , are all consecutive? i.e, that all 9's have 8,7,6 etc below and 1, 2,3, etc. above?

[@SudokuSleuth]

Hopefully you can see that the longest thermometer, which is all 9 cells, must have the digits 1-9 consecutively on it Once you place the 9 cell thermometer, you need to place the 8 cell thermometer, and it cannot start with a 1 as you’ve already used that elsewhere in row 9 on the 9 cell thermometer. So the 8 cell thermometer has to be the digits 2-9, and therefore every digit is consecutive Now rinse and repeat!

[@nicksharpe7924]

Ah ha! Thanks.@@SudokuSleuth

[@simonwstrong]

Very neat solve, direct and clearly explained. I prefer this to the CtC solve.

[@SudokuSleuth]

Glad you liked it!

[@ryuuguu01]

Spoiler ----- When I realized that all the columns were just n~9 with 1~n stacked on top it felt good.